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Neutrosophic Multigroups and Applications

Author

Listed:
  • Vakkas Uluçay

    (Department of Mathematics, Gaziantep University, 27310 Gaziantep, Turkey)

  • Memet Şahin

    (Department of Mathematics, Gaziantep University, 27310 Gaziantep, Turkey)

Abstract

In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization of multisets and neutrosophic sets. In this paper, we proposed a algebraic structure on neutrosophic multisets is called neutrosophic multigroups which allow the truth-membership, indeterminacy-membership and falsity-membership sequence have a set of real values between zero and one. This new notation of group as a bridge among neutrosophic multiset theory, set theory and group theory and also shows the effect of neutrosophic multisets on a group structure. We finally derive the basic properties of neutrosophic multigroups and give its applications to group theory.

Suggested Citation

  • Vakkas Uluçay & Memet Şahin, 2019. "Neutrosophic Multigroups and Applications," Mathematics, MDPI, vol. 7(1), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:1:p:95-:d:198500
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    References listed on IDEAS

    as
    1. Florentin Smarandache & Mehmet Şahin & Abdullah Kargın, 2018. "Neutrosophic Triplet G-Module," Mathematics, MDPI, vol. 6(4), pages 1-9, April.
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    Cited by:

    1. Correia, Inês C. & Ferreira, Fernando A.F. & Zopounidis, Constantin & Ferreira, Neuza C.M.Q.F., 2024. "Urban expansion effects on real estate ecosystems: Identification and neutrosophic analysis of causal dynamics," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).
    2. Vaz-Patto, Constança M.R.P. & Ferreira, Fernando A.F. & Govindan, Kannan & Ferreira, Neuza C.M.Q.F., 2024. "Rethinking urban quality of life: Unveiling causality links using cognitive mapping, neutrosophic logic and DEMATEL," European Journal of Operational Research, Elsevier, vol. 316(1), pages 310-328.

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